This article focuses on the research and development of innovative polymer-concrete composites for the manufacture of precision machine tool frames and critical mechanical engineering components. The relevance of this work stems from the need to replace traditional cast iron and cement concrete with materials with superior damping properties and thermal stability. The polymer matrix used in this study was ED-20 epoxy-diane resin, modified with (FAM) furan resin and cured with polyethylenepolyamine (PEPA), which together ensured minimal linear shrinkage (less than 0.5–1%) during polymerization. The focus was on the effect of multimodal filler distribution, including quartz sand, gabbro, and basalt, as well as reinforcing additives such as silicon carbide and fiberglass, on the final performance characteristics of the material. Experimental studies determined the key physical and mechanical parameters of the obtained samples. The results showed that the optimized composition (Smp_001) exhibited compressive strength up to 92.3 MPa, significantly exceeding that of standard high-strength concrete. It was established that the use of silicon carbide and glass fiber promotes the formation of a dense heterogeneous microstructure characterized by extremely low porosity (1.2–2.5%) and record-low water absorption (less than 0.05%). These characteristics guarantee high dimensional stability of the frames during prolonged contact with process fluids and cutting fluids. The scanning electron microscopy (SEM) and (EDS) energy dispersive X-ray spectroscopy methods confirmed the dense packing and high degree of interaction of the polymer matrix with the crystalline phases of the filler. This condition of the interfacial boundaries guarantees stable stress transfer throughout the entire volume of the material, which minimizes the risk of local damage during operation. The study confirmed that the developed material has vibration damping properties 6–10 times more effective than gray cast iron, a critical factor in improving machining accuracy on modern metal-cutting machines. The scientific novelty of the study lies in its substantiation of the synergistic effect of the combined use of basalt fillers and silicon carbide to achieve the precision properties of a structural material. Its practical significance is confirmed by the possibility of producing large-scale parts by casting without the need for complex finishing, opening up new prospects for modernizing the machine tool industry.